Question

What is the slope and y-intercept of this line `15x - 3y = -90`?

Answer 1

See a solution process below:

Explanation:

This equation is in Standard Linear form. The standard form of a linear equation is: `color(red)(A)x + color(blue)(B)y = color(green)(C)`

Where, if at all possible, `color(red)(A)`, `color(blue)(B)`, and `color(green)(C)`are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

The slope of an equation in standard form is: `m = -color(red)(A)/color(blue)(B)`

The `y`-intercept of an equation in standard form is: `color(green)(C)/color(blue)(B)`

`color(red)(15)x - color(blue)(3)y = color(green)(-90)`

Or

`color(red)(15)x + (color(blue)(-3)y) = color(green)(-90)`

Therefore:

• The slope of the line is: `m = (-color(red)(15))/color(blue)(-3) = 5`

• The `y`-intercept is: `color(green)(C)/color(blue)(B) = (-90)/(-3) = 30` or `(0, 30)`